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50=4x^2+2x
We move all terms to the left:
50-(4x^2+2x)=0
We get rid of parentheses
-4x^2-2x+50=0
a = -4; b = -2; c = +50;
Δ = b2-4ac
Δ = -22-4·(-4)·50
Δ = 804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{201}}{2*-4}=\frac{2-2\sqrt{201}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{201}}{2*-4}=\frac{2+2\sqrt{201}}{-8} $
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